Stejskal’s formula for multiple-pulsed diffusion MRI

Abstract A fundamental theoretical result for diffusion MRI is the formula by Stejskal showing that the diffusion NMR signal is proportional to the Fourier transform of the diffusion displacement probability density function. Here this result is extended to multiple-pulsed diffusion MRI (MP-dMRI) by...

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Bibliographic Details
Published inMagnetic resonance imaging Vol. 33; no. 9; pp. 1182 - 1186
Main Author Jensen, Jens H
Format Journal Article
LanguageEnglish
Published Netherlands Elsevier Inc 01.11.2015
Subjects
Algorithms
Cumulant expansion
Diffusion Magnetic Resonance Imaging - methods
Diffusion MRI
Fourier Analysis
Humans
Image Interpretation, Computer-Assisted - methods
Imaging, Three-Dimensional - methods
Kurtosis
Multiple wave vector
Pulsed field gradient
q-space
Radiology
q-space
Diffusion MRI
Multiple wave vector
Kurtosis
Cumulant expansion
Pulsed field gradient
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Summary:Abstract A fundamental theoretical result for diffusion MRI is the formula by Stejskal showing that the diffusion NMR signal is proportional to the Fourier transform of the diffusion displacement probability density function. Here this result is extended to multiple-pulsed diffusion MRI (MP-dMRI) by using a higher dimensional q-space formalism to express the diffusion-weighted signal for a sequence with N diffusion wave vectors in terms of a Fourier transform of a diffusion displacement probability density function in a 3N-dimensional space. As an illustration of the application of this extended version of Stejskal’s formula, it is used to analyze the cumulant expansion of the signal magnitude for MP-dMRI.
Bibliography:ObjectType-Article-1
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ISSN:0730-725X
1873-5894
DOI:10.1016/j.mri.2015.07.001